1400
14002 = 63 + 653 + 1193.
14002 = (1)(2 + 3 + 4 + 5)(6 + 7 + 8 + ... + 19)(20 + 21 + 22 + ... + 44),
14002 = (1)(2 + 3 + 4 + 5 + 6)(7)(8 + 9 + 10 + ... + 167),
14002 = (1 + 2 + 3 + 4)(5)(6 + 7 + 8 + 9 + 10)(11 + 12 + 13 + ... + 45),
14002 = (1 + 2 + 3 + 4)(5 + 6 + 7 + ... + 11)(12 + 13)(14 + 15 + 16 + ... + 21),
14002 = 175 x 176 + 176 x 177 + 177 x 178 + 178 x 179 + ... + 223 x 224.
by Yoshio Mimura, Kobe, Japan
1401
The 4-by-4 magic squares consisting of different squares with constant 1401:
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Page of Squares : First Upload February 16, 2010 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1404
481k + 624k + 1404k + 1716k are squares for k = 1,2,3 (652, 23532, 904152).
14042 = (1)(2)(3)(4 + 5)(6)(7 + 8 + 9 + ... + 110),
14042 = (1)(2)(3)(4 + 5 + 6 + ... + 9)(10 + 11 + 12 + ... + 17)(18 + 19 + 20 + 21),
14042 = (1)(2 + 3 + 4 + 5 + 6 + 7)(8)(9 + 10 + 11 + ... + 17)(18 + 19 + 20 + 21),
14042 = (1 + 2)(3)(4)(5 + 6 + 7 + 8)(9 + 10 + 11 + ... + 17)(18),
14042 = (1 + 2)(3)(4 + 5 + 6 + ... + 12)(13)(14 + 15 + 20 + ... + 25),
14042 = (1 + 2)(3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 19)(20 + 21 + 22 + ... + 28),
14042 = (1 + 2 + 3)(4 + 5)(6)(7 + 8 + 9 + ... + 110),
14042 = (1 + 2 + 3)(4 + 5 + 6 + ... + 9)(10 + 11 + 12 + ... + 17)(18 + 19 + 20 + 21).
by Yoshio Mimura, Kobe, Japan
1405
14052 = 1974025, a square with different digits.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1406
The 4-by-4 magic squares consisting of different squares with constant 1406:
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Page of Squares : First Upload February 16, 2010 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1407
14072 = 1512 + 1532 + 1552 + 1572 + 1582 + 1592 + ... + 2472.
14072 = 44 + 44 + 184 + 374.
The 4-by-4 magic squares consisting of different squares with constant 1407:
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Page of Squares : First Upload January 29, 2007 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1408
14082 = (12 + 7)(22 + 7)(112 + 7)(132 + 7) = (12 + 7)(32 + 7)(92 + 7)(132 + 7)
= (12 + 7)(92 + 7)(532 + 7) = (22 + 7)(32 + 7)(92 + 7)(112 + 7) = (22 + 7)(52 + 7)(752 + 7)
= (32 + 7)(112 + 7)(312 + 7) = (92 + 7)(112 + 7)(132 + 7).
by Yoshio Mimura, Kobe, Japan
1410
66k + 210k + 1230k + 1410k are squares for k = 1,2,3 (542, 18842, 683642).
The 4-by-4 magic squares consisting of different squares with constant 1410:
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Page of Squares : First Upload February 16, 2010 ; Last Revised April 22, 2011
by Yoshio Mimura, Kobe, Japan
1411
207417k + 378148k + 632128k + 773228k are squares for k = 1,2,3 (14112, 10878812, 8819780032).
Page of Squares : First Upload April 22, 2011 ; Last Revised April 22, 2011by Yoshio Mimura, Kobe, Japan
1412
14122 = 733 + 803 + 1033.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1413
14132 = 363 + 733 + 1163.
The 4-by-4 magic square consisting of different squares with constant 1413:
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Page of Squares : First Upload July 7, 2008 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1414
14142 = 1999396, a square with odd digits except the last digit 6.
1414 = (12 + 22 + 32 + ... + 2522) / (12 + 22 + 32 + ... + 222).
14142 = 1999396 with 1936 = 442 (1999396 is a square pegged by 9).
Page of Squares : First Upload January 29, 2007 ; Last Revised August 24, 2013by Yoshio Mimura, Kobe, Japan
1415
14152 = 2002225, a square with jusut 3 kinds of digits : 0, 2 and 5.
The square root of 1415 is 37.61..., 37 = 62 + 12.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1416
A cubic polynomial :
(X + 14162)(X + 15682)(X + 25832) = X3 + 33372X2 + 58915922X + 57350039042.
The 4-by-4 magic square consisting of different squares with constant 1416:
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Page of Squares : First Upload January 29, 2007 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1417
1 / 1417 = 0.000705716302046577275935...,
72 + 05712 + 6302 + 22 + 0462 + 5772 + 2752 + 9352 = 14172.
14172 = (32 + 4)(3932 + 4).
793k + 1417k + 2977k + 11713k are squares for k = 1,2,3 (1302, 121942, 12793302).
Page of Squares : First Upload January 29, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1418
14182 = 2010724, a zigzag square.
14182± 3 are primes.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1419
14192 = (52 + 8)(2472 + 8).
14195 = 5753233191123099 :
52 + 72 + 52 + 32 + 22 + 32 + 32 + 12 + 92 + 12 + 122 + 302 + 92 + 92 = 1419.
The 4-by-4 magic squares consisting of different squares with constant 1419:
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Page of Squares : First Upload December 8, 2008 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1420
14202± 3 are primes.
Page of Squares : First Upload January 16, 2014 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1421
14212 = (137 + 138 + 139 + 140 + 141 + 142 + 143)2 + (144 + 145 + 146 + 147 + 148 + 149 + 150)2.
665k + 1421k + 2401k + 5117k are squares for k = 1,2,3 (982, 58662, 3885702).
The 4-by-4 magic square consisting of different squares with constant 1421:
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Page of Squares : First Upload January 29, 2007 ; Last Revised April 22, 2011
by Yoshio Mimura, Kobe, Japan
1422
14222 = (59 + 60 + 61)2 + (62 + 63 + 64)2 + (65 + 66 + 67)2 + ... + (128 + 129 + 130)2.
14222 = 503 + 933 + 1033.
14222 = 2022084, a square with even digits.
126k + 538k + 1050k + 1422k are squares for k = 1,2,3 (562, 18522, 647362).
The 4-by-4 magic squares consisting of different squares with constant 1422:
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Page of Squares : First Upload January 29, 2007 ; Last Revised April 22, 2011
by Yoshio Mimura, Kobe, Japan
1423
14232 = 2024929, 2 + 0 * 2 + 49 * 29 = 2 * 0 + 2 + 49 * 29 = 1423.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1425
14252 = 2030625, a zigzag square.
14252 = 253 + 953 + 1053.
The 4-by-4 magic squares consisting of different squares with constant 1425:
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Page of Squares : First Upload January 29, 2007 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1426
1 / 1426 = 0.00070126227208..., 72 + 02 + 122 + 62 + 22 + 272 + 202 + 82 = 1426,
1 / 1426 = 0.00070126227208..., 72 + 0122 + 62 + 22 + 272 + 202 + 82 = 1426.
The 5-by-5 magic squares consisting of different squares with constant 1426:
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Page of Squares : First Upload January 29, 2007 ; Last Revised October 19, 2009
by Yoshio Mimura, Kobe, Japan
1427
The 5-by-5 magic square consisting of different squares with constant 1427:
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Page of Squares : First Upload October 19, 2009 ; Last Revised October 19, 2009
by Yoshio Mimura, Kobe, Japan
1428
14282 = 2039184, a square with different digits.
14282 = 263 + 633 + 1213.
The integral triangle of sides 2169, 2897, 4760 (or 313, 43911, 44210) has square area 14282.
14282 = (1)(2)(3 + 4)(5 + 6 + 7 + ... + 12)(13 + 14 + 15)(16 + 17 + 18),
14282 = (1)(2)(3 + 4 + 5 + ... + 53)(54 + 55 + 56 + ... + 65),
14282 = (1 + 2 + 3 + ... + 16)(17)(18 + 19 + 20 + ... + 45),
14282 = (1 + 2 + 3 + ... + 6)(7)(8)(9 + 10 + 11 + ... + 59),
14282 = (1 + 2 + 3 + ... + 6)(7)(8 + 9)(10 + 11 + 12 + ... + 41),
14282 = (1 + 2 + 3 + ... + 6)(7)(8 + 9 + 10 + ... + 24)(25 + 26).
by Yoshio Mimura, Kobe, Japan
1429
A cubic polynomial :
(X + 842)(X + 8192)(X + 11682) = X3 + 14292X2 + 9640682X + 803537282.
by Yoshio Mimura, Kobe, Japan
1430
14302 = (1)(2 + 3)(4)(5 + 6)(7 + 8 + 9 + ... + 136),
14302 = (1 + 2 + 3 + 4)(5 + 6)(7 + 8 + 9 + ... + 19)(20 + 21 + 22 + 23 + 24).
14302 = (43 + 44)2 + (45 + 46)2 + (47 + 48)2+ (49 + 50)2 + (51 + 52)2 + ...+ (145 + 146)2.
376090k + 439010k + 441870k + 787930k are squares for k = 1,2,3 (14302, 10725002, 8445437002).
The 4-by-4 magic squares consisting of different squares with constant 1430:
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Page of Squares : First Upload January 29, 2007 ; Last Revised April 22, 2011
by Yoshio Mimura, Kobe, Japan
1431
14312 = 13 + 23 + 33 + 43 + 53 + ... + 533.
14312 = 93 + 363 + 1263.
14314 = 4193325113121, and 42 + 12 + 92 + 32 + 322 + 52 + 112 + 32 + 122 + 12 = 1431.
The 4-by-4 magic square consisting of different squares with constant 1431:
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Page of Squares : First Upload January 29, 2007 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1432
14322 is a zigzag square.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1433
14332 = 2053489, a square with different digits.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1434
14342 = S2(57) + S2(181), where S2(n) = 12 + 22 + 32 + ... + n2.
14342 = 93 + 943 + 1073.
The sum of the squares of divisors of 1434 is a square, 16902.
The 4-by-4 magic squares consisting of different squares with constant 1434:
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Page of Squares : First Upload January 29, 2007 ; Last Revised November 1, 2011
by Yoshio Mimura, Kobe, Japan
1435
Komachi equation: 14352 = 1232 * 42 * 52 * 62 * 72 / 82 / 92.
Page of Squares : First Upload July 27, 2010 ; Last Revised July 27, 2010by Yoshio Mimura, Kobe, Japan
1437
14372 is a zigzag square.
94842k + 468462k + 593481k + 908184k are squares for k = 1,2,3 (14372, 11855252, 10304195312).
140826k + 425352k + 547497k + 951294k are squares for k = 1,2,3 (14372, 11855252, 10510692212).
The 4-by-4 magic square consisting of different squares with constant 1437:
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Page of Squares : First Upload January 29, 2007 ; Last Revised April 22, 2011
by Yoshio Mimura, Kobe, Japan
1439
The 5-by-5 magic square consisting of different squares with constant 1439:
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Page of Squares : First Upload October 19, 2009 ; Last Revised October 19, 2009
by Yoshio Mimura, Kobe, Japan
1440
14402 = (22 - 1)(172 - 1)(492 - 1) = (22 - 1)(32 -1)(42 - 1)(72 - 1)(112 - 1)
= (22 - 1)(42 - 1)(72 - 1)(312 - 1) = (22 - 1)(52 - 1)(92 - 1)(192 - 1) = (32 - 1)(42 - 1)(72 - 1)(192 - 1)
= (42 - 1)(52 - 1)(72 - 1)(112 - 1) = (72 - 1)(112 - 1)(192 - 1) = (92 - 1)(1612 - 1).
14402 = 103 + 893 + 1113 = 403 + 963 + 1043.
14402 = (1)(2)(3 + 4 + 5)(6 + 7 + 8 + 9)(10 + 11 + 12 + 13 + 14)(15 + 16 + 17),
14402 = (1 + 2 + 3 + ... + 15)(16)(17 + 18 + 19)(20).
Cubic polynomials :
(X + 6002)(X + 14402)(X + 15472) = X3 + 21972X2 + 25633202X + 13366080002,
(X + 14402)(X + 16122)(X + 58592) = X3 + 62452X2 + 128752922X + 136003795202.
The quadratic polynomial -1440X2 + 10920X - 9191 takes the values 172, 832, 1032, 1072, 972, 672 at X = 1, 2,..., 6,
Page of Squares : First Upload January 29, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1441
14412 = 2076481, a square with different digits.
14412 = 93 + 963 + 1063.
Page of Squares : First Upload January 29, 2007 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1442
14422 = 2079364, a square with different digits.
14422 = 2079364 with 207936 = 4562 and 4 = 22.
64890k + 232162k + 803194k + 979118k are squares for k = 1,2,3 (14422, 12891482, 12122692122).
The 4-by-4 magic squares consisting of different squares with constant 1442:
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Page of Squares : First Upload January 29, 2007 ; Last Revised April 22, 2011
by Yoshio Mimura, Kobe, Japan
1443
14432 = 72 + 262 + 452 + 642 + 832 + 1022 + 1212 + ... + 4822.
The 4-by-4 magic square consisting of different squares with constant 1443:
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Page of Squares : First Upload January 29, 2007 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1444
The square of 38.
14442 = 2085136, a square with different digits.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1445
14452 = (43 + 44 + 45 + ... + 59)2 + (60 + 61 + 62 + ... + 76)2.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1446
Loop of length 35 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
1446 - 2312 - 673 - 5365 - ... - 5114 - 2797 - 10138 - 1446
(Note f(1446) = 142 + 462 = 2312, f(2312) = 232 + 122 = 673, etc. See 37)
14462 = 2090916, a zigzag square.
The 4-by-4 magic squares consisting of different squares with constant 1446:
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The 5-by-5 magic square consisting of different squares with constant 1446:
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Page of Squares : First Upload January 29, 2007 ; Last Revised February 16, 2010
by Yoshio Mimura, Kobe, Japan
1447
14472 = 20903809 is a zigzag square.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1448
14482 = 2096704 is a zigzag square.
14482 = 523 + 783 + 1143.
Page of Squares : First Upload January 29, 2007 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1449
A cubic polynomial :
(X + 10562)(X + 11482)(X + 14492) = X3 + 21292X2 + 25647722X + 17566053122.
14492 = 403 + 843 + 1133.
14492 = (1 + 2)(3 + 4 + 5 + ... + 11)(12 + 13 + 14 + ... + 149).
14492 = (42 + 5)(82 + 5)(382 + 5).
14495 = 6387661996482249 : 62 + 32 + 82 + 72 + 62 + 62 + 192 + 92 + 62 + 42 + 82 + 22 + 242 + 92 = 1449.
The 4-by-4 magic squares consisting of different squares with constant 1449:
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Page of Squares : First Upload January 29, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1450
14502 = 683 + 793 + 1093.
14502 = (22 + 1)(32 + 1)(122 + 1)(172 + 1) = (52 + 4)(112 + 4)(242 + 4).
1450k + 12818k + 24186k + 45646k are squares for k = 1,2,3 (2902, 532442, 105528682).
The 5-by-5 magic squares consisting of different squares with constant 1450:
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Page of Squares : First Upload July 7, 2008 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1451
14512 = 2105401, 210 * 5 + 401 = 1451.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1452
14522 = (52 + 8)(62 + 8)(382 + 8).
14522 = 773 + 883 + 993.
Page of Squares : First Upload July 7, 2008 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1455
14552 = 23 + 733 + 1203 = 253 + 873 + 1133.
Komachi equation: 14552 = 92 / 82 / 72 / 62 * 54322 * 102.
The 4-by-4 magic squares consisting of different squares with constant 1455:
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The 5-by-5 magic squares consisting of different squares with constant 1455:
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Page of Squares : First Upload July 7, 2008 ; Last Revised July 27, 2010
by Yoshio Mimura, Kobe, Japan
1456
14562 = (12 + 3)(52 + 3)(72 + 3)(192 + 3).
Page of Squares : First Upload December 14, 2013 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1457
14572 = 183 + 733 + 1203.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1458
14582 = 134 + 134 + 214 + 374 = 274 + 274 + 274 + 274 = 95 + 95 + 95 + 95 + 185 = 96 + 96 + 96 + 96.
14582 = (1)(2 + 3 + 4)(5 + 6 + 7 + ... + 22)(23 + 24 + 25 + ... + 49),
14582 = (1 + 2)(3)(4)(5 + 6 + 7 + ... + 13)(14 + 15 + 16 + ... + 40),
14582 = (1 + 2)(3)(4)(5 + 6 + 7 + ... + 22)(23 + 24 + 25 + ... + 31).
The 4-by-4 magic squares consisting of different squares with constant 1458:
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Page of Squares : First Upload January 29, 2007 ; Last Revised March 1, 2010
by Yoshio Mimura, Kobe, Japan
1459
14592 = 30 + 36 + 37 + 312 + 313.
Page of Squares : First Upload August 29, 2011 ; Last Revised August 29, 2011by Yoshio Mimura, Kobe, Japan
1460
170k + 370k + 830k + 1130k are squares for k = 1,2,3 (502, 14602, 455002).
Page of Squares : First Upload April 22, 2011 ; Last Revised April 22, 2011by Yoshio Mimura, Kobe, Japan
1461
311193k + 400314k + 487974k + 935040k are squares for k = 1,2,3 (14612, 11702612, 10138974752).
The 4-by-4 magic square consisting of different squares with constant 1461:
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Page of Squares : First Upload March 1, 2010 ; Last Revised April 22, 2011
by Yoshio Mimura, Kobe, Japan
1462
14622 = 2137444, 2 + 13 * 7 * 4 * 4 + 4 = 1462.
S2(1462) = S2(5) x S2(6) x S2(85), where S2(n) = 12 + 22 + 32 + ... + n2.
14622 = 393 + 503 + 1253.
Page of Squares : First Upload January 29, 2007 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1463
14632 = 2140369, a square with different digits.
14632 = (21 + 22 + 23 + 24 + 25 + 26 + 27)2 + (28 + 29 + 30 + 31 + 32 + 33 + 34)2 + (35 + 36 + 37 + 38 + 39 + 40 + 41)2 + ... + (91 + 92 + 93 + 94 + 95 + 96 + 97)2.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1464
14642 = 243 + 713 + 1213 = 723 + 953 + 973.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1466
1 / 1466 = 0.0006821282401..., 62 + 82 + 22 + 12 + 282 + 242 + 02 + 12 = 1466,
1 / 1466 = 0.0006821282401..., 62 + 82 + 22 + 12 + 282 + 242 + 012 = 1466.
14662 = 493 + 993 + 1023 = 18 + 28 + 38 + 38 + 48 + 58 + 68.
Page of Squares : First Upload January 29, 2007 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1467
14672 = (1 + 2 + 3 + ... + 162)(163).
The 4-by-4 magic square consisting of different squares with constant 1467:
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Page of Squares : First Upload January 29, 2007 ; Last Revised March 1, 2010
by Yoshio Mimura, Kobe, Japan
1468
14682 = 44 + 84 + 164 + 384.
Page of Squares : First Upload July 7, 2008 ; Last Revised July 7, 2008by Yoshio Mimura, Kobe, Japan
1469
399568k + 430417k + 593476k + 734500k are squares for k = 1,2,3 (14692, 11120332, 8653423612).
Page of Squares : First Upload April 22, 2011 ; Last Revised April 22, 2011by Yoshio Mimura, Kobe, Japan
1470
14702 = 353 + 493 + 1263.
14702 = (12 + 6)(22 + 6)(62 + 6)(272 + 6) = (12 + 6)(32 + 6)(62 + 6)(222 + 6)
= (122 + 6)(1202 + 6) = (22 + 6)(32 + 6)(1202 + 6) = (62 + 6)(82 + 6)(272 + 6).
210k + 1470k + 14490k + 27930k are squares for k = 1,2,3 (2102, 315002, 49833002).
994k + 1470k + 2338k + 4802k are squares for k = 1,2,3 (982, 56282, 3573082).
430k + 740k + 1470k + 1585k are squares for k = 1,2,3 (652, 23252, 874252).
14702 = (1)(2)(3 + 4)(5 + 6 + 7 + 8 + 9)(10)(11 + 12 + 13 + ... + 31),
14702 = (1)(2)(3 + 4)(5 + 6 + 7 + 8 + 9)(10 + 11)(12 + 13 + 14 + ... + 23),
14702 = (1)(2 + 3)(4 + 5 + 6 + ... + 24)(25 + 26 + 27 + ... + 59),
14702 = (1)(2 + 3)(4 + 5 + 6 + ... + 31)(32 + 33 + 34 + ... + 52),
14702 = (1)(2 + 3 + 4 + 5)(6 + 7 + 8)(9 + 10 + 11 + 12)(13 + 14 + 15 + 22),
14702 = (1)(2 + 3 + 4 + ... + 8)(9)(10)(11 + 12 + 13 + ... + 38),
14702 = (1)(2 + 3 + 4 + ... + 8)(9 + 10 + 11 + ... + 351),
14702 = (1)(2 + 3 + 4)(5 + 6 + 7 + 8 + 9)(10)(11 + 12 + 13 + ... + 38),
14702 = (1 + 2)(3 + 4 + 5 + ... + 9)(10)(11 + 12 + 13 + ... + 59),
14702 = (1 + 2 + 3 + ... + 14)(15 + 16 + 17 + ... + 20)(21 + 22 + 23 + ... + 28),
14702 = (1 + 2 + 3 + ... + 24)(25 + 26 + 27 + ... + 122),
14702 = (1 + 2 + 3 + 4 + 5 + 6)(7 + 8 + 9 + ... + 13)(14)(15 + 16 + ... + 20).
14702 = 309 x 310 + 311 x 312 + 313 x 314 + 315 x 316 + ... + 347 x 348.
The 4-by-4 magic squares consisting of different squares with constant 1470:
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The 5-by-5 magic squares consisting of different squares with constant 1470:
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Page of Squares : First Upload January 29, 2007 ; Last Revised December 14, 2013
by Yoshio Mimura, Kobe, Japan
1471
The 5-by-5 magic squares consisting of different squares with constant 1471:
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Page of Squares : First Upload October 28, 2009 ; Last Revised October 28, 2009
by Yoshio Mimura, Kobe, Japan
1472
14722 = (12 + 7)(192 + 7)(272 + 7) = (12 + 7)(32 + 7)(42 + 7)(272 + 7)
= (12 + 7)(42 + 7)(52 + 7)(192 + 7) = (32 + 7)(52 + 7)(652 + 7) = (42 + 7)(112 + 7)(272 + 7).
A cubic polynomial :
(X + 5042)(X + 9992)(X + 14722) = X3 + 18492X2 + 17223122X + 7411461122.
14722 = 84 + 164 + 324 + 324.
Page of Squares : First Upload January 29, 2007 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1473
14732 = 2169729, 22 + 12 + 62 + 92 + 72 + 22 + 92 = 162.
The 4-by-4 magic square consisting of different squares with constant 1473:
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Page of Squares : First Upload January 29, 2007 ; Last Revised March 1, 2010
by Yoshio Mimura, Kobe, Japan
1474
14742± 3 are primes.
The 4-by-4 magic square consisting of different squares with constant 1474:
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The 5-by-5 magic squares consisting of different squares with constant 1474:
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Page of Squares : First Upload October 28, 2009 ; Last Revised January 16, 2014
by Yoshio Mimura, Kobe, Japan
1475
14752 = 2175625, a zigzag square.
14752 = 2175625, 22 + 12 + 72 + 52 + 62 + 22 + 52 = 122.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1476
14762± 5 are primes.
14762 = 204 + 204 + 304 + 324.
14762 = (1)(2 + 3 + 4)(5 + 6 + 7 + ... + 36)(37 + 38 + 39 + ... + 45).
14762 = (12 + 8)(22 + 8)(1422 + 8) = (102 + 8)(1422 + 8) = (22 + 8)(192 + 8)(222 + 8).
Page of Squares : First Upload January 29, 2007 ; Last Revised January 16, 2014by Yoshio Mimura, Kobe, Japan
1477
14772 = 2181529, a zigzag square.
A cubic polynomial :
(X + 5122)(X + 8372)(X + 11042) = X3 + 14772X2 + 11649122X + 4731125762.
125545k + 186102k + 773948k + 1095934k are squares for k = 1,2,3 (14772, 13603172, 13372772772).
206780k + 454916k + 728161k + 791672k are squares for k = 1,2,3 (14772, 11860312, 9925956952).
14772 = 2181529 appears in the decimal expressions of e:
e = 2.71828•••2181529••• (from the 15006th digit)
(2181529 is the sixth 7-digit square in the expression of e.)
by Yoshio Mimura, Kobe, Japan
1478
1 / 1478 = 0.000676..., 676 = 262.
226k + 610k + 822k + 1478k are squares for k = 1,2,3 (562, 18122, 634242).
Page of Squares : First Upload January 29, 2007 ; Last Revised April 22, 2011by Yoshio Mimura, Kobe, Japan
1479
1 / 1479 = 0.000676..., 676 = 262.
The 4-by-4 magic square consisting of different squares with constant 1479:
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The 5-by-5 magic squares consisting of different squares with constant 1479:
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Page of Squares : First Upload January 29, 2007 ; Last Revised March 1, 2010
by Yoshio Mimura, Kobe, Japan
1480
Loop of length 10 by the function f(N) = ... + c2 + b2 + a2 where N = ... + 1002c + 100b + a:
1480 - 6596 - 13441 - 2838 - ... - 6833 - 5713 - 3418 - 1480
(Note f(1480) = 142 + 802 = 6596, f(6596) = 652 + 962 = 13441, etc. See 1268)
14802 = (12 + 4)(22 + 4)(2342 + 4) = (62 + 4)(2342 + 4).
Page of Squares : First Upload October 9, 2008 ; Last Revised December 14, 2013by Yoshio Mimura, Kobe, Japan
1481
14815 = 7124842897431401 : 72 + 122 + 42 + 82 + 42 + 22 + 82 + 92 + 72 + 42 + 312 + 42 + 02 + 12 = 1481.
Page of Squares : First Upload December 8, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
1482
1482k + 2850k + 32718k + 79914k are squares for k = 1,2,3 (3422, 864122, 233538122).
1482k + 6630k + 15418k + 19734k are squares for k = 1,2,3 (2082, 259482, 34124482).
The 4-by-4 magic squares consisting of different squares with constant 1482:
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Page of Squares : First Upload March 1, 2010 ; Last Revised April 22, 2011
by Yoshio Mimura, Kobe, Japan
1484
14842 = 73 + 173 + 1303.
14845 = 7197298330471424 : 72 + 192 + 72 + 292 + 82 + 32 + 32 + 02 + 42 + 72 + 12 + 42 + 22 + 42 = 1484.
Page of Squares : First Upload July 7, 2008 ; Last Revised December 8, 2008by Yoshio Mimura, Kobe, Japan
1485
14852 = 2205225, a square with just 3 kinds of digits.
14852 = 65 + 95 + 125 + 185.
14852 = (1)(2 + 3)(4 + 5 + 6 + ... + 14)(15 + 16 + 17 + ... + 95),
14852 = (1)(2 + 3 + 4 + ... + 16)(17 + 18 + 19 + ... + 181),
14852 = (1)(2 + 3 + 4)(5 + 6)(7 + 8)(9)(10 + 11 + 12 + ... + 20),
14852 = (1)(2 + 3 + 4)(5 + 6)(7 + 8 + 9 + 10 + 11)(12 + 13 + 14 + ... + 33),
14852 = (1)(2 + 3 + 4)(5 + 6 + 7 + ... + 10)(11)(12 + 13 + 14 + ... + 33),
14852 = (1 + 2)(3 + 4 + 5 + ... + 1212),
14852 = (1 + 2)(3 + 4 + 5 + ... + 24)(25 + 26 + 27 + ... + 74),
14852 = (1 + 2)(3 + 4 + 5 + ... + 8)(9)(10 + 11 + 12 + ... + 15)(16 + 17),
14852 = (1 + 2)(3 + 4 + 5 + ... + 8)(9)(10 + 11 + 12)(13 + 14 + 15 + 16 + 17),
14852 = (1 + 2)(3 + 4 + 5 + ... + 8)(9 + 10 + 11 + 12 + 13)(14 + 15 + 16 + ... + 31).
14852 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + ... + 543.
14852 + 14862 + 14872 + ... + 15122 = 15132 + 15142 + 15152 + ... + 15392.
The 4-by-4 magic squares consisting of different squares with constant 1485:
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Page of Squares : First Upload January 29, 2007 ; Last Revised September 9, 2011
by Yoshio Mimura, Kobe, Japan
1486
The 5-by-5 magic squares consisting of different squares with constant 1486:
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Page of Squares : First Upload November 10, 2009 ; Last Revised November 10, 2009
by Yoshio Mimura, Kobe, Japan
1487
14872 = 84 + 144 + 174 + 384.
1 / 1487 = 0.0006724..., 6724 = 822.
14872 = 30 + 31 + 33 + 34 + 38 + 39 + 310 + 312 + 313.
Page of Squares : First Upload January 29, 2007 ; Last Revised August 29, 2011by Yoshio Mimura, Kobe, Japan
1488
14882 = 2214144, a square with just 3 kinds of digits 1, 2 and 4.
1488k + 2356k + 9145k + 11036k are squares for k = 1,2,3 (1552, 146012, 14578372).
Page of Squares : First Upload January 29, 2007 ; Last Revised April 22, 2011by Yoshio Mimura, Kobe, Japan
1489
14892 = 2217121, a square with just 3 kinds of digits 1, 2 and 7.
14892 = 2217121, 22 + 22 + 12 + 72 + 12 + 22 + 12 = 82.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1490
S2(417) + S2(1479) = S2(1490), where S2(n) = 12 + 22 + ... + n2.
The 5-by-5 magic square consisting of different squares with constant 1490:
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Page of Squares : First Upload January 29, 2007 ; Last Revised November 10, 2009
by Yoshio Mimura, Kobe, Japan
1491
14913 = 3314613771, and 32 + 32 + 12 + 42 + 62 + 12 + 372 + 72 + 12 = 1491.
14912 = 2223081 appears in the decimal expressions of π:
π = 3.14159•••2223081••• (from the 45924th digit)
The 4-by-4 magic squares consisting of different squares with constant 1491:
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Page of Squares : First Upload December 1, 2008 ; Last Revised March 1, 2010
by Yoshio Mimura, Kobe, Japan
1492
14922 = 2226064, a square with even digits.
14922 = 2226064, 22 + 22 + 22 + 62 + 02 + 62 + 42 = 102.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1494
The 4-by-4 magic squares consisting of different squares with constant 1494:
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The 5-by-5 magic square consisting of different squares with constant 1494:
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Page of Squares : First Upload November 10, 2009 ; Last Revised March 1, 2010
by Yoshio Mimura, Kobe, Japan
1495
1495 = (12 + 22 + 32 + ... + 10002) / (12 + 22 + 32 + ... + 872).
14952 = S2(144) + S2(154), where S2(n) = 12 + 22 + ... + n2.
Komachi equations:
14952 = 12 * 232 / 42 * 52 * 62 * 782 / 92 = 12 * 232 * 452 / 62 * 782 / 92.
14952 = (22 + 23 + 24 + ... + 44)2 + (45 + 46 + 47 + ... + 67)2.
The 5-by-5 magic squares consisting of different squares with constant 1486:
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Page of Squares : First Upload January 29, 2007 ; Last Revised July 27, 2010
by Yoshio Mimura, Kobe, Japan
1496
14962 = S2(116) + S2(172), where S2(n) = 12 + 22 + ... + n2.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1497
The 4-by-4 magic square consisting of different squares with constant 1497:
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Page of Squares : First Upload March 1, 2010 ; Last Revised March 1, 2010
by Yoshio Mimura, Kobe, Japan
1498
14982 = 2244004, a square with just 3 kinds of even digits 0, 2 and 4.
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan
1499
(14992 + 7) = (42 + 7)(52 + 7)(62 + 7)(82 + 7).
Page of Squares : First Upload January 29, 2007 ; Last Revised January 29, 2007by Yoshio Mimura, Kobe, Japan